Qualocation for a singularly perturbed boundary value problem |
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Authors: | Hans-G Roos Zorica Uzelac |
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Institution: | 1. Institute of Numerical Mathematics, Technical University of Dresden, Mommsenstrasse 13, Dresden, D-01062, Germany;2. Department for Fundamental Disciplines, Faculty of Technical Sciences, Trg D. Obradovi?a 6, 21000 Novi Sad, Serbia |
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Abstract: | A singularly perturbed one-dimensional two point boundary value problem of reaction–convection–diffusion type is considered. We generate a C0-collocation-like method by combining Galerkin with an adapted quadrature rule. Using Lobatto quadrature and splines of degree r, we prove on a Shishkin mesh for the qualocation method the same error estimate as for the Galerkin technique. The result is also important for the practical realization of finite element methods on Shishkin meshes using quadrature formulas. We report the results of numerical experiments that support the theoretical findings. |
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Keywords: | 65L10 65L12 65L60 |
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